Question

b. the linear function $f(x)$ generates the ordered pairs shown in the table.

$x$	-2	-1	0	1	2
$f(x)$	-2	1	4	7	10

drag and drop the numbers below into the boxes to complete the sentence.
-9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
the function that models the data in the table is $f(x) = \square x + \square$.

Explanation:

Step1: Find the slope (m)

The slope \( m \) of a linear function \( f(x) = mx + b \) can be found using two points \((x_1, f(x_1))\) and \((x_2, f(x_2))\) with the formula \( m=\frac{f(x_2)-f(x_1)}{x_2 - x_1} \). Let's use the points \((0, 4)\) and \((1, 7)\).
\( m=\frac{7 - 4}{1 - 0}=\frac{3}{1}=3 \)

Step2: Find the y - intercept (b)

For a linear function \( f(x)=mx + b \), when \( x = 0 \), \( f(0)=b \). From the table, when \( x = 0 \), \( f(0)=4 \), so \( b = 4 \).

Step3: Write the function

So the linear function is \( f(x)=3x + 4 \)

Answer:

The function is \( f(x)=\boldsymbol{3}x+\boldsymbol{4} \)